Ellipsometry is a technique that is being used to determine the polarization state of light. It is widely applied to accurately and precisely quantify changes in polarization of a probe beam after interaction with a sample. The measurement is contact free and generally non-destructive. The rate at which measurements can be performed depends, in principle, only on the speed of the data acquisition hardware, such as optical detectors, and on the light budget for the application. This makes ellipsometry not only accurate and precise but also inherently fast as well as relatively inexpensive. The available advantages of cost, precision, and accuracy allow ellipsometric techniques to be used for non-destructive high volume applications that would otherwise be too expensive, too time consuming, in-accurate, or in general be complex and non-trivial to realize.
An important example for the successful application of ellipsometry can be found in the semiconductor industry, where it is being used to measure the success rate (yield) of material deposition processes as well as micro-lithographic patterning processes for computer chip and memory production.
Ellipsometric measurements can be done in transmission or reflection, however, for applications that are specifically targeted at surface processes reflection measurements are more sensitive. In a typical configuration, an incident beam of light is polarized to contain only photons of a certain, known state of polarization. After reflection by the sample—which usually occurs at non-normal incidence and, for best sensitivity, close to Brewster's angle—the polarization of the probe beam has changed to be of some new and unknown state, which is generally an elliptical mode. Linear and circular modes are two special cases of elliptical modes. The polarization of the reflected beam is then measured by the detection arm of the instrument and the difference between detected polarization of the reflected beam and known polarization of the incident beam is being computed. The difference in polarization is attributed to the cumulative effect of the optical properties of the sample, which depends on the presence and thickness of one or multiple overlayers and the effective refractive index and absorption coefficient of overlayer and bulk material(s). Other sample properties to which ellipsometry is sensitive are (1) structural dimensions within surface and bulk material, where it is used for instance to measure the spacing of periodic ridges in so called critical dimensions analysis, (2) alloy composition, (3) crystallinity, etc. With models and assumptions that are suitable for the specimen, the desired structural and material properties may be inferred and quantified from the difference signal. The derived quantities are then compared to target values for process control purposes, or they may be analyzed for their fundamental physical significance for instance for material research and development purposes.
A typical example of an ellipsometer of the common rotating polarizer type is shown in FIG. 1. Light from a source 100 is polarized via polarizer 110 and is incident on the sample 120. The sample may include one or more overlayers 122. Rotation of the polarizer causes the polarization state to rotate as a function of time, which means that the magnitude of incident p- and s-polarized light is being modulated as the polarizer turns. The modulation of the incident light occurs at twice the polarizer rotation rate, since the polarizer has a 2-fold symmetry, i.e., azimuth angles of 0° and 180° result in the same transmitted intensity. The modified polarization state of the reflected beam is being projected onto the transmission axis of an analyzer 130, and the intensity that is transmitted by the analyzer is measured with a detector 140 as a function of polarizer azimuth. The Fourier Transform of the detected signal (harmonic analysis) yields two non-zero frequency components, of which the amplitude and the relative phase contain the information that we seek. Even though the same information can be obtained with so called NULL-ellipsometry, where the polarizer is not spinning, the type of modulation measurement described here has found widespread acceptance due to its simplicity and because it is better suited for continuous, fast operation than NULL-ellipsometry.
By denoting the reflective properties of the sample as rp and rs for light that is polarized parallel and perpendicular to the plane of incidence, respectively, the physical quantities that lend themselves to optical far field detection are (1) |rp|2+|rs|2 which is the normalized reflected intensity, (2) |rp|2−|rs|2 which is the difference between p- and s-polarized intensity, and (3) the phase shift Δ between p- and s-polarized constituents of the beam, which was introduced upon reflection by the sample. The term far-field refers to the region that is many wavelengths away from the source of the radiation, in this case the sample surface. Since optical wavelengths are small, on the order of nanometers, virtually all common optical applications involve only far-field detection. Without resorting to interferometric techniques, the most information that is available from such a measurement is the intensity for two orthogonal polarizations and the relative phase-shift between them.
The rotating polarizer system described above returns the intensity (1), the intensity excess of one polarization over the other (2), and (3) the cosine of the phase shift between p- and s-polarized light, i.e. cos(Δ). Not readily accessible are incident intensity and an overall phase. Equivalent information is obtained from a rotating analyzer system, where the polarizer is fixed and the analyzer rotates. It can be shown that the system is symmetric under time reversal, i.e. the direction of propagation does not matter in principle, except that source and detector are reversed. However, it is important to emphasize that both, rotating polarizer and rotating analyzer ellipsometers (RPE/RAE) can only return cos(Δ) and not Δ itself, which has significant yet not necessarily obvious implications for the application.
Whenever the relative phase shift between rp and rs happens to be in the vicinity of 0, π, 2π, etc. cos(Δ) assumes an extremum and hence is independent of a variation in Δ, which renders the system insensitive to small changes, for instance in overlayer thickness. This is a particular disadvantage for measuring very thin films, or whenever the thickness of an overlayer meets a resonance condition, i.e. for which the phase shift between p- and s-waves is an integer multiple of π. In these situations, all data is lost. In addition, the cosine is a symmetric function around Δ=0 and hence rectifies the phase shift, so that it is not possible to tell the handedness of the reflected elliptical mode.
The weakness of RPE/RAEs is resolved by introducing a rotating waveplate as shown in FIG. 2. Such a system is called a rotating compensator ellipsometer (RCE) and features a spinning quarter-waveplate 230, also sometimes called a compensator, while keeping polarizer and analyzer stationary. The quarter waveplate 230 is constructed out of a birefringent material, such as MgF2, and is made of specific thickness to retard orthogonal polarization directions by 90°, i.e., a quarter of a wavelength. Modulation of the beam is introduced by rotating the direction of the 90° phase shift, hence the spinning waveplate. The intensity is measured in much the same way as in the RPE system, except that it is now a function of waveplate azimuth. The detector readout must be synchronized to the rotation of the compensator instead of the polarizer.
An RCE returns both cosine and sine of the relative phase A, which is equivalent to A itself, and therefore the sensitivity of the measurement does not depend on sample properties as in an RPE or RAE system. Whenever the cosine assumes a maximum, sine goes through zero, which means that sensitivity lost in one coefficient is re-distributed to the other coefficient, respectively, maintaining the overall information content of the signal. Hence an RCE is also called a complete system, since it returns all of the available optical information, while RPE/RAEs are considered incomplete systems. RPE/RAEs have proven to be simple and useful in the past, however, RCEs are being regarded as the more modern and more desirable systems due to the enhancement in diagnostic power, and their robustness and high precision that derives from stationary polarizer and analyzer prisms.
A new dimension is added to ellipsometry when measurements are done over a spectrum of wavelengths instead of a single wavelength, such as produced by a broadband light source, e.g. a Xenon arc lamp. All wavelengths are transmitted simultaneously through the system in a “white” beam and the different wavelength constituents are separated in space after the analyzer by means of a dispersive element, such as a grating or a prism, and detected for instance with an array detector such as a charge-coupled device (CCD) or a linear photo diode array (PDA). Such a broadband system, called a spectroscopic ellipsometer, offers the advantage of providing sample properties like the dielectric function of a material as a function of wavelength or, equivalently, energy. Further, spectroscopic ellipsometry is essential for samples with stratified single or multiple overlayers, which are encountered regularly in the manufacturing process of computer chips and memory devices. The penetration depth of light depends on the wavelength, so that the short wavelength part of the spectrum can be used to measure overlayer dielectric function as if it was bulk material, while the longer wavelengths penetrate deeper to reach the underlying interface, and together with knowledge of the dielectric function of the overlayer material provide the layer thickness. With thickness and dielectric function, the layer on top of the substrate can be characterized comprehensively.
Broadband operation is essential for many applications, however, rotating compensator systems are not ideally suited for it. The difficulty encountered with RCE operation is a consequence of the fact that the retardation of the waveplate depends on the wavelength of light approximately as 1/λ,λ being the wavelength, yet the retardation needs to be that of a quarter wave over the entire spectral range for best sensitivity. The retardation is more generally given by Δn(λ)t /λ, with Δn being a difference in refractive index for the two orthogonal directions of the birefringent material and t being an effective thickness of the waveplate. For the sake of argument, a weak dependence of Δn on wavelength may be assumed.
With the retardation increasing towards the short wavelength end of the spectrum, the sensitivity of the RCE gradually decreases and is reduced to that of an equivalent rotating polarizer system when it approaches 180°. Reducing the wavelength further, the sensitivity initially increases, assumes a second maximum at 270° but then hits a dead zone around 360° retardation, for which an RCE returns no phase information at all but becomes a simple off-axis reflectometer, which is even less useful than an RPE. Rotating polarizer systems on the other hand do not suffer from a wavelength dependence of sensitivity in that sense, since they are constructed out of essentially dispersion free components and need not contain a waveplate at all.
An example of a rotating compensator ellipsometer is described in U.S. Pat. No. 5,973,787, entitled “Broadband Spectroscopic Rotating Compensator Ellipsometer,” granted to David E. Apnes of Apex, N.C. and Jon Opsal of Livermore, Calif. and assigned to Therma-Wave Corporation of Fremont, Calif., which discloses how a single-rotating-compensator system can be designed to cover a relatively wide range of retardation values, even though it does not have optimal sensitivity over the entire wavelength range and is limited in bandwidth. Extension of the available bandwidth into the extreme UV below 190 nm while retaining the visible to IR sensitivity is impossible with the prescribed broadband ellipsometer and the presently available waveplates.
One could, in principle, circumvent the wavelength restrictions of a rotating-compensator system by constructing it with an achromatic compensator, such as a Fresnel rhomb. However, these devices are non-trivial and expensive to manufacture, they are significantly bigger and heavier than a standard waveplate, and they feature unevenly distributed moments about the optical axis. Hence achromatic retarders are more difficult to use in a continuously, fast-rotating configuration than standard waveplates. Another practical requirement is that the exit beam be co-linear to the entrance beam, which is also non-trivial in the case of thick components, such as an achromatic retarder.
In summary, current single rotating compensator designs employ a waveplate that works reasonably well over a wide spectral range, yet, due to the dispersive nature of the material out of which the waveplate is constructed (typically MgF2), the sensitivity is compromised at either the extremely short-or long wavelengths, or at both extremes. Specifically, 100% loss of the signal occurs at wavelengths where the retardation either approaches 0° or 360°, and partial loss of information occurs in the vicinity of 180° retardation.
Thus there is a need in the art of spectroscopic ellipsometry to overcome the bandwidth limitations of rotating compensator systems without reintroducing the well known shortfalls of rotating polarizer ellipsometers. One would like to have a complete system, such as an RCE, to detect all available optical information over the available wavelength range with optimal sensitivity. Such a system is proposed in this application.